The principal block of a ℤℓ-spets and Yokonuma type algebras

Kessar, Radha; Malle, Gunter; Semeraro, Jason

doi:10.2140/ant.2023.17.397

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The principal block of a ${\mathbb Z}_{\ell}$-spets and Yokonuma type algebras

Radha Kessar, Gunter Malle and Jason Semeraro

Vol. 17 (2023), No. 2, 397–433

DOI: 10.2140/ant.2023.17.397

Abstract

We formulate conjectures concerning the dimension of the principal block of a $ℤ_{ℓ}$ -spets (as defined in our earlier paper), motivated by analogous statements for finite groups. We show that these conjectures hold in certain situations. For this we introduce and study a Yokonuma type algebra for torus normalisers in $ℓ$ -compact groups which may be of independent interest.

Keywords

$\ell$-adic reflection groups, Yokonuma type algebra, principal block, spetses

Mathematical Subject Classification

Primary: 16G30, 20C08, 20C20, 20F55, 20G40

Secondary: 20D20, 55R35

Milestones

Received: 30 June 2021

Revised: 9 March 2022

Accepted: 11 April 2022

Published: 24 March 2023

Authors

Radha Kessar
Department of Mathematics City, University of London London United Kingdom

Gunter Malle
Fachbereich Mathematik TU Kaiserslautern Kaiserslautern Germany

Jason Semeraro
Heilbronn Institute for Mathematical Research, Department of Mathematics University of Leicester Leicester United Kingdom

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Vol. 17, No. 2, 2023